5^th Generation

Row

Column

Node

Appendix references

Concept

Depends on/

Related to

Contribution

5

1

PP_5,1

[33]

Soil

water retention

PP_4,1

The relation of pore-size to particle-size distribution is certain. Large pores can be associated with large and smaller particles (page 8). Consequently, pore-size and particle size distribution are related to measured soil water retention (page 5)²

5

2

PP_5,2

[26]

Soil

texture

PP_4,2

Evidence suggests that soil texture influences the content, the distribution and the composition of soil organic matter (SOM) (pages 207, 208). Consequently, soil organic matter is related to soil texture.³

5

3

PP_5,3

[16]

Capillary

pressure

PP_4,3

Effective liquid saturation (S_e) depends on Capillary pressure (P_c), according to Corey approximation equation (equation 10, page 10)

$S_e={\left(\frac{c}{P_c}\right)}^2$ , where the terms, definitions and dimensions of $\left(S_e,c,P_c\right)$ are presented in detail in the below terminology (Table A8) of the Appendix. For clarification purposes, (c) is a constant.

5

4

ASTM_5,4

[14]

Capillary

Pressure head

PP_4,4

Interfacial tension (γ) depends on capillary pressure head (h_c), according to the implicit function:

$\begin{array}{l}\gamma =\left(\frac{z}{t^2}\right)\ast f(\left(\frac{z}{q\ast t}\right),\left(Sh\right),\left(\frac{z}{v_z\ast t}\right),\left(Sc\right),\left(\frac{\mu }{\psi \ast t}\right),\left(\frac{t\ast \mu }{{\rho }_s\ast z^2}\right),\left(Ri\right),\\ \left(\frac{z}{h_c}\right),\left(\frac{z^2}{t\ast D}\right),\left(Re\right),\left(\frac{z}{S\ast t^{0.5}}\right))\end{array}$

where the terms, definitions and dimensions of $\left(\gamma ,z,t,q,Sh,v_z,Sc,\mu ,\psi ,{\rho }_s,Ri,h_c,D,Re,S\right)$ are presented in detail in the below terminology (Table A8) of the Appendix. For clarification purposes, (q) refers to infiltration rate and (S) refers to the sorptivity. Rayleigh’s method of indices was deployed along with the echelon matrix procedure as an additional confirmation method.

5

5

ASTM_5,5

[6]

Thermal

diffusivity

PP_4,1

Soil mass density (ρ_s) depends on thermal diffusivity (D_th), according to implicit function:

$\begin{array}{l}{\rho }_s=(\left(\frac{\lambda \ast T^3}{D_{th}^3\ast {\left(\frac{\text{d}T}{\text{d}z}\right)}^2}\right)*f\left(\left(\frac{D_{th}^2\ast {\left(\frac{\text{d}T}{\text{d}z}\right)}^2}{C\ast T^3}\right),\left(\frac{T^2}{t\ast D_{th}\ast {\left(\frac{\text{d}T}{\text{d}z}\right)}^2}\right),\left(\frac{T^3}{V_s\ast {\left(\frac{\text{d}T}{\text{d}z}\right)}^3}\right)\right)\\ \left(\frac{\lambda \ast T^6}{D_{th}^3\ast M_s\ast {\left(\frac{\text{d}T}{\text{d}z}\right)}^5}\right),\left(\frac{\lambda \ast T}{D_{th}\ast \left(\frac{\text{d}T}{\text{d}z}\right)\ast k_{th}}\right),\Phi ,n)\end{array}$

where the terms, definitions and dimensions of $\left({\rho }_s,\lambda ,T,D_{th},z,C,v_s,M_s,k_{th},\Phi ,n\right)$ are presented in detail in the below terminology (Table A8) of the Appendix. For clarification purposes, (Φ) is the total porosity and (n) is pore size distribution index. Rayleigh’s method of indices was deployed along with the echelon matrix procedure as an additional confirmation method.